（-1x1/2）+(-1/2x1/3)+(-1/3x1/4)+.+(-1/99x1/100)=?

（-1x1/2）+(-1/2x1/3)+(-1/3x1/4)+.+(-1/99x1/100)=?
（-1x1/2）+(-1/2x1/3)+(-1/3x1/4)+.+(-1/99x1/100)=?

（-1x1/2）+(-1/2x1/3)+(-1/3x1/4)+.+(-1/99x1/100)=?
先提取负号,
1x1/2=1-1/2=1/2
1/2x1/3=1/2-1/3=1/6
.
所以原式=—【1-1/2+1/2-1/3+.+1/99-1/100】=—【1-1/100】=99/100

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